login
A125759
Number of n-indecomposable polyominoes.
7
1, 6, 34, 448, 13384, 684236, 52267569
OFFSET
1,2
COMMENTS
A polyomino is called n-indecomposable if it cannot be partitioned (along cell boundaries) into two or more polyominoes each with at least n cells.
MacKinnon incorrectly implies that the sequence is 1,6,44.
MacKinnon only allows polyominoes with >= n cells, leading to A125709 and A125753.
The polyominoes with < 2n cells are uninteresting, leading to A126742 and A126743.
There is a sense in which n-decomposable polyominoes with >3n-2 cells are also uninteresting: they are precisely the "n-spiders", where an n-spider is a polyomino with a cell whose removal splits it into 4 components each with <n cells. - Peter Pleasants, Feb 18 2007
FORMULA
a(n) = A125709(n) + Sum_{i=1..n-1} A000105(i).
EXAMPLE
The six 2-indecomposable polyominoes:
......................X.
X..XX..XXX..XX..XXX..XXX
.............X...X....X.
CROSSREFS
Sequence in context: A245466 A362627 A284330 * A062819 A230246 A092336
KEYWORD
nonn,more
AUTHOR
EXTENSIONS
a(4) and a(5) from Peter Pleasants, Feb 13 2007
a(6) and a(7) from David Applegate, Feb 16 2007
STATUS
approved